Q:

# How Do You Use a Formula for Angles in a Triangle?

A:

Three laws can be used to find the sides and angles of almost any triangle: the Law of Angles, the Law of Sines, and the Law of Cosines. The Law of Angles means that all three angles of a triangle add up to 180 degrees. The Law of Sines is that the ratio of each side to the sine of its opposite angle is equal: a/sin(A) = b/sin(B) = c/sin(C). The Law of Cosines works when all sides are known.

## Keep Learning

If the only quantities you know are angles, the triangle cannot be solved because you need to know at least one of the sides. The equation for the Law of Cosines is c^2 = a^2 + b^2 - 2abcos(C). By substituting the values for the sides and taking the inverse cosine, you can derive the angle opposite side c and proceed from there. C is usually the longest side, but not always. As an example, assume you have a triangle with sides 3. 4 and 5. Substituting these values yields 5^2 = 3^2 + 4^2 - 2(3)(4)cos(C), or 25 = 9 + 16 - 24cos(C). By solving and taking the inverse cosine, you can determine that one of the angles is 90 degrees.

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